How does a RF mixer circuit work?

Discussion in 'Electronic Basics' started by Bill Bowden, Jan 27, 2005.

  1. Bill Bowden

    Bill Bowden Guest

    I've never really understood how a mixer circuit in a typical radio
    receiver produces the sum and difference frequencies between
    the incoming RF signal and the local oscillator. I understand
    it requires a non-linear circuit, but I can't quite see
    how the signals subtract to produce the IF frequency.

    For example, if the RF input is 1 mHz and the IF is 455 kHz, the local
    oscillator should be running at 1.455 mHz. How do we combine
    1 mHz and 1.455 mHz to get 455 kHz?

    -Bill
    Bill Bowden, Jan 27, 2005
    #1
  2. Bill Bowden wrote:
    > I've never really understood how a mixer circuit in a typical radio
    > receiver produces the sum and difference frequencies between
    > the incoming RF signal and the local oscillator. I understand
    > it requires a non-linear circuit, but I can't quite see
    > how the signals subtract to produce the IF frequency.
    >
    > For example, if the RF input is 1 mHz and the IF is 455 kHz, the local
    > oscillator should be running at 1.455 mHz. How do we combine
    > 1 mHz and 1.455 mHz to get 455 kHz?
    >


    The basic idea is the standard trig identity:

    sin(x)sin(y) = [cos(x-y) - cos(x+y)]/2.

    So, one has to generate a sin(x)sin(y), i.e. a multiplication.

    If a device is non-linear it may typically be represented by:

    Vo = a + b.Vi^2 + c.Vi^3 ++...

    If Vi = VpSin(w1t) + VpSin(w2t), i.e. a simple sum of two input signals,
    then

    Vo = a + b.(VpSin(w1t) + VpSin(w2t))^2 ++...

    Epanding this gives a VpSin(w1t).VpSin(w2t) term


    Kevin Aylward

    http://www.anasoft.co.uk
    SuperSpice, a very affordable Mixed-Mode
    Windows Simulator with Schematic Capture,
    Waveform Display, FFT's and Filter Design.
    Kevin Aylward, Jan 27, 2005
    #2
  3. Bill Bowden

    Andrew Holme Guest

    Bill Bowden wrote:
    > I've never really understood how a mixer circuit in a typical radio
    > receiver produces the sum and difference frequencies between
    > the incoming RF signal and the local oscillator. I understand
    > it requires a non-linear circuit, but I can't quite see
    > how the signals subtract to produce the IF frequency.
    >
    > For example, if the RF input is 1 mHz and the IF is 455 kHz, the

    local
    > oscillator should be running at 1.455 mHz. How do we combine
    > 1 mHz and 1.455 mHz to get 455 kHz?
    >
    > -Bill


    Kevin Aylward has already posted the trig identity, showing how the
    multiplication of sine waves produces sum and difference frequencies.
    It's also worth pointing out that not all mixers are driven with sine
    waves: often, the local oscillator input is a square wave.

    Switching mixers, such as diode ring mixers, multiply the input by +1
    for half the LO cycle and -1 for the other half. The diode "switches"
    simply reverse the connections to the mixer output transfomer.

    If you have a signal f1 and square wave LO drive f2, since the latter
    is the sum of an infinite series of odd harmonics, it's like having an
    infinite number of local oscillators! The mixer outputs are f1 +/- f2,
    f1 +/- 3f2, f1 +/- 5f2 e.t.c. The unwanted products are removed by the
    post-mixer filter.
    Andrew Holme, Jan 27, 2005
    #3
  4. Bill Bowden

    Guest

    , Jan 27, 2005
    #4
  5. Bill Bowden

    john jardine Guest

    "Bill Bowden" <> wrote in message
    news:...
    > I've never really understood how a mixer circuit in a typical radio
    > receiver produces the sum and difference frequencies between
    > the incoming RF signal and the local oscillator. I understand
    > it requires a non-linear circuit, but I can't quite see
    > how the signals subtract to produce the IF frequency.
    >
    > For example, if the RF input is 1 mHz and the IF is 455 kHz, the local
    > oscillator should be running at 1.455 mHz. How do we combine
    > 1 mHz and 1.455 mHz to get 455 kHz?
    >
    > -Bill
    >


    'Mixers' are just phase sensitive rectifiers.
    If you want physical insight as to how that difference frequency somehow
    turns up, It can be handy to just to draw out 10 cycles of a 50:50 square
    wave a piece of squared paper (2 square high, 2 squares low).
    Pretend this is the local oscillator running at say 1MHz. This now switches
    the rectifier device that will be rectifying the incoming RF input signal
    and somehow generating those sum and difference frequencies (and many
    others).
    The rectifier can be something as simple as a CD4066 ON/OFF switch. The
    rectifier does not *have* to be a diode or some strange device with a non
    linear bend in it. In fact, the ON/OFF type switch is the best of them all.

    For the RF input signal, draw a line of (say) 7 square waves underneath the
    local oscillor signal, 3 square high, 3 squares low, =666kHz. Start them at
    the same point but make sure they are correctly sized (phased) relative to
    the top line.

    Now for the rectification/mixing/multiplying/modulating action ...
    Draw a third "0V" output line under the previous two.
    Every time the local oscillator is high then the RF signal passes through
    to the output (is rectified), so just copy to the output line, the segment
    of the 'RF' square wave that sits under the local oscillator during it's
    high periods.

    After doing all 10 then look at the resulting mishmash of blocks and half
    blocks and visually average them (a human RC low pass filter).
    Notice there is a low frequency undulating component present (about 3 cycles
    over the run ='340kHz')). This is the 'oddball' I.F frequency.
    regards
    john
    john jardine, Jan 27, 2005
    #5
  6. Bill Bowden

    Guest

    Well, the basic idea is: signal can be "modulated"
    into higher frequencies or "demoluated" from lower
    frequencies. In plain English, the reason to do that is:
    in the space we live, only some portion of the spectrum
    can carried the signal with less attenuation. So, we
    would like to use that portion of spectrum to transmit
    the signal.

    You might try
    http://www.ScienceOxygen.com/Trigonometrics.html
    http://www.SicenceOxygen.com/signal188.html

    for more information. It is with a collection of links
    so that you can find the associated information
    from there.
    , Jan 28, 2005
    #6
  7. Bill Bowden

    Bill Bowden Guest

    > If you want physical insight as to how that difference
    > frequency somehow turns up, It can be handy to just to
    > draw out 10 cycles of a 50:50 square wave a piece of
    > squared paper (2 square high, 2 squares low) .


    John,

    Yes, that's a good illustration. My graph paper wasn't
    quite wide enough for 10 cycles, so I drew an 8 cycle
    square wave for the oscillator (using 4 squares per cycle)
    and 5.33 cycles for the RF signal (using 6 squares).
    The result plots out to 2 high squares, followed by 6 low
    squares, followed by 1 high and 3 low for a total of
    12 squares. The sequence then repeats, so the frequency
    of the combined pattern works out to 2.66 cycles, which
    is the difference of 8 and 5.33.
    Very good illustration.

    -Bill
    Bill Bowden, Jan 29, 2005
    #7
  8. Bill Bowden

    foTONICS VIP Member

    Joined:
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    neat, I didn't know that
    foTONICS, Nov 13, 2013
    #8

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